Problem: Solve for $x$ and $y$ using elimination. ${x-2y = -3}$ ${-x-5y = -32}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-7y = -35$ $\dfrac{-7y}{{-7}} = \dfrac{-35}{{-7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {x-2y = -3}\thinspace$ to find $x$ ${x - 2}{(5)}{= -3}$ $x-10 = -3$ $x-10{+10} = -3{+10}$ ${x = 7}$ You can also plug ${y = 5}$ into $\thinspace {-x-5y = -32}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(5)}{= -32}$ ${x = 7}$